My associate recently had a sudden and tragic thing happen with one of her patients. The dog was a geriatric basset hound that I had also seen previously, and had even done surgery to remove several large skin tumors. This time she was seen for a routine checkup and vaccines. I briefly looked at her because the owner wanted some smaller skin masses removed and wanted me to do it in the near future. My associate is a very good, experienced doctor who has been practicing a few years longer than I have and has done a good bit of emergency work. The dog appeared in good condition with no obvious serious problems, and walked out of the clinic with her tail wagging and in good spirits.
About eight hours later the owner rushed her to the emergency clinic, where she presented deceased on arrival. The emergency doctor noted a lot of free blood in her abdomen and a softball-sized mass palpable. The owner declined a necropsy, so nothing definitive could be determined about the cause of death.
The owner is concerned that my associate missed something on the exam. However, as I said, she is a very good, experienced doctor, and would be unlikely to miss something as large as the other doctor noted. Also, there was nothing done to her that would have caused sudden internal bleeding, even a vaccine reaction (which doesn't cause spontaneous hemorrhage). I can see some of the owner's concern, as she brought in an old but healthy dog, we did some services, and several hours later her dog suddenly bled to death. I would be asking questions myself, and wondering what had happened.
Really, this appears to be a case of bad timing and coincidence. Yes, coincidences do happen, and an event like this doesn't mean that a doctor was negligent or caused the problem. A previously unknown splenic tumor may have ruptured, filling part of the spleen in the bargain, or the spleen may have suddenly twisted. Conditions like this can happen and are generally unpredictable. Often the only sign of such a disorder is sudden death, as tragic as that may be. I know it's easy to blame the last person to see the pet, and most certainly that should be investigated, but that isn't the only answer. Unfortunately in this case we have only speculation as to what happened, as the owner declined the necropsy. But I'm convinced that my associate didn't miss or cause this problem.
If something like this ever happens to you, talk to the doctor about it and listen to what they have to say. Also, feel free to ask opinions of other vets, making sure the first vet isn't covering something up. But be willing to accept that such events can happen through nobody's fault, and it likely would have happened without any visit or services. It was just bad luck and happenstance that it happened on the same day.